Question

Line A passes through points (-1, 5) and (3, -1). Line B passes through points (7, 2) and (6, -1).

Answer 1

Answer:

          At (5, -4)

Step-by-step explanation:

The slope of a line that passes through two given points: $m=\dfrac{y_2-y_1}{x_2-x_1}$

The equation of the line that passes through given point with a slope of m:  

y - y₁ = m(x - x₁)

Line A:

 $m=\dfrac{-1-5}{3-(-1)}=\dfrac{-6}4=-\dfrac32$

$y-5=-\frac32(x+1)\\\\y=-\frac32(x+1)+5$

Line B:

 $m=\dfrac{-1-2}{6-7}=\dfrac{-3}{-1}=3$

$y-2=3(x-7)\\\\y=3(x-7)+2$

Point of intersect means the same coordinates x and y.

So:

       $3(x-7)+2=-\frac32(x+1)+5\\\\3x-21+2=-\frac32x-\frac32+5\\\\3x-19=-\frac32x+\frac72\\\\6x-38=3x+7\\\\6x+3x=7+38\\\\9x=45\\\\x=5\\\\y=3(5-7)+2=3(-2)+2=-4$